PROVED (LEAN)
This has been solved in the affirmative and the proof verified in Lean.
A set $A\subset \mathbb{N}$ is primitive if no member of $A$ divides another. Is the sum\[\sum_{n\in A}\frac{1}{n\log n}\]maximised over all primitive sets when $A$ is the set of primes?
Erdős
[Er35] proved that this sum always converges for a primitive set. Lichtman
[Li23] proved that the answer is yes. An alternative, simpler, proof is given by Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang, and Tao
[ABLLPSTT26].
See also
[1196].
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This page was last edited 12 May 2026. View history
Additional thanks to: Jared Lichtman
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #164, https://www.erdosproblems.com/164, accessed 2026-05-22
